Higher education institutions will also be expected to improve drop-out rates under the latest set of outcome agreements.
Across the sector, universities will be expected to increase the proportion of pupils from the most deprived postcode areas by 2.5 percentage points by 2016/17 compared to 2011/12.
The Scottish Funding Council also expects the number of students moving from college to the second or third year of a university degree to increase to more than 4000 by 2016/17 - a 41% rise from 2011/12.
The move comes after some of Scotland's oldest universities were accused of dragging their feet over moves to recruit more students from deprived backgrounds.
In 2012 The Herald revealed that St Andrews University - where Prince William studied - recruited only 13 students from the most deprived backgrounds in Scotland in 2010/11.
The second-lowest proportion was at Aberdeen University, with 51, followed by Edinburgh University, with 91.
Michael Russell, the Education Secretary, said: "Outcome agreements give a greater transparency to the work our universities and colleges do."